Properties

Label 139650.jb
Number of curves $2$
Conductor $139650$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("jb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 139650.jb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.jb1 139650ck1 \([1, 0, 0, -12983188, -31668533758]\) \(-131661708271504489/159475479581250\) \(-293158292144601269531250\) \([]\) \(23224320\) \(3.1966\) \(\Gamma_0(N)\)-optimal
139650.jb2 139650ck2 \([1, 0, 0, 109559687, 594629247617]\) \(79116632600119361351/128876220703125000\) \(-236908726398468017578125000\) \([]\) \(69672960\) \(3.7459\)  

Rank

sage: E.rank()
 

The elliptic curves in class 139650.jb have rank \(0\).

Complex multiplication

The elliptic curves in class 139650.jb do not have complex multiplication.

Modular form 139650.2.a.jb

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + 3 q^{11} + q^{12} + 5 q^{13} + q^{16} + 3 q^{17} + q^{18} - q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.